Building recommendation systems via federated learning (FL) is a new emerging challenge for next-generation Internet service. Existing FL models share item embedding across clients while keeping the user embedding private and local on the client side. However, identical item embedding cannot capture users' individual differences in perceiving the same item and may lead to poor personalization. Moreover, dense item embedding in FL results in expensive communication costs and latency. To address these challenges, we propose Federated Recommendation withAdditive Personalization (FedRAP), which learns a global view of items via FL and a personalized view locally on each user. FedRAP encourages a sparse global view to save FL's communication cost and enforces the two views to be complementary via two regularizers. We propose an effective curriculum to learn the local and global views progressively with increasing regularization weights. To produce recommendations for a user, FedRAP adds the two views together to obtain a personalized item embedding. FedRAP achieves the best performance in FL setting on multiple benchmarks. It outperforms recent federated recommendation methods and several ablation study baselines. Our code is available at https://github.com/mtics/FedRAP.